1. These lines look pretty different, don't they?
What is Slope?
Lines are used to keep track of lots of info -- like how much money a company makes.  Just off the top of your head, which of the lines above would you want to describe the profits of YOUR company?  Whether the line is tilted up or down, all of the sudden, gets REALLY important!
These lines look pretty different, don't they?

2. Slope of a Line
In a coordinate plane, the slope of a straight line is defined by the change in y divided by the change in x.

3. Positive Slope (Uphill)
Pierre The Mountain Climbing Ant
For slopes, Pierre is going to walk on the lines from left to right
Uphill slopes are positive slopes. The slope will be a positive number like 5 or 2 3

4. Negative Slope (Downhill)
Downhill slopes are negative slopes. The slope will be a negative number like -7 or -1 3

5. Zero & Undefined Slope Zero Slope Undefined Slope
Slope of a Straight Line x y
Zero Slope
Horizontal Line
Horizontal lines have a slope of 0. x y
Undefined Slope
Vertical Line
A vertical line has an undefined slope.

6. Finding the Slope of a Line
Using a Graph
Let's look at the line going through the points
                                               
Slope is
      
(rise over run)

7. Finding the Slope of a Line Using a Graph
To get from the point (-2, -1) to the point (4, 3),  you rise up 4... and run 6.
The slope is
                                               
(Notice that the slope goes uphill and    is a positive number)

8. Finding the Slope of a Line
Using a Graph
For             , you can "rise" up or down... but,
you ALWAYS "run" to the right.  ALWAYS!

9. Finding the Slope of a Line
Using a Graph
Let's find the slope of this line:

10. Finding the Slope of a Line
Using a Graph
                                        
                                     

11. Finding the Slope of a Line
Using Formula
Definition of Slope of a Line
The slope of any nonvertical line that contains the points with coordinates (x1, y1) and (x2, y2) is defined by the difference ratio
where x2  x1.

12. Finding the Slope of a Line
Example 1:
Find the slope of the line that passes through (3, 6) and (1, 2).

13. Finding the Slope of a Line
Example 2:
Find the slope of the line that passes through
(-2, 2) and (3, 4).

14. Finding the Slope of a Line
Example 3:
Find the slope of the line that passes through (0, 0) and (3, -3).

15. Finding the Slope of a Line
Example 4:
Find the slope of the line that passes through
(-1, 2) and (3, 2).

16. Finding the Slope of a Line
Example 5:
Find the slope of the line that passes through (2, 4) and (2, 1).